SEG Houston 2009 International Exposition and Annual Meeting

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1 Yueming Ye *1, Ru-Shan Wu and Zhenchun Li 2 Modeling and Imaging Laboratory, IGPP, University of California, Santa Cruz, CA Summary Migration with data acquired on surface with irregular topography can be extrapolated from the highest surface based on one-way wavefield propagator. We fill with near surface velocity the area between the highest surface level and the irregular surface. At every depth, the corresponding seismic data are added if receivers or source exist. We use the local-cosine-bases (LCB) beamlet propagator which improves the image quality at the near irregular surface area because of its windowed reference velocity. We apply the local exponential frame (LEF) decomposition to obtain the image and amplitude correction factor in local wavenumber domain and then transform them into local angle domain after all the shot summation. The influence of irregular topography has been eliminated during the continuation process. We test our method with Model94 which has the highest elevation nearly 1800 meters. Compare with the imaging results without aperture correction or with Auto-vertical gain control (AGC), it has significant improvement in image quality, especially, the deep area with weak illumination. Introduction Irregular topography offers a big challenge for traditional horizon-based stacking methods during migration and imaging in the mountain areas like western China. There are some ways to eliminate the influence of irregular surface. Reshef (1991) proposed a method by depth migration from the highest irregular surface and added the data where receivers exist. Beasley and Lynn (1992) proposed a zero-speed layer concept, which would also remove the impact of irregular surface by inserting a virtual layer with low speed between the irregular surface and datum surface, However, it is not stable in area with sharp irregularity. Due to the limited seismic data acquisition aperture in reality, the inverse-propagated waves cannot completely recover the scattered wave field and will render distortion to the amplitude of the image. This problem may even worse in area with irregular topography. Wu et al. (2004) proposed an amplitude correction method in the local angle domain (LAD) for aperture correction. Wavefield decomposition into LAD can be done by local slant stack (LSS) (e.g., Xie and Wu 2002; Xie et al., 2004, 2006). Their numerical examples showed significant improvement in the images. Beamlet decomposition (e.g., Wu et al., 2000) can decompose the wavefield into local waves, which are simultaneously localized in the space and direction. It is faster to obtain the LAD image and amplitude correction factor (Cao and Wu 2008) by decomposition in the local wavenumber domain (LWD) using LEF decomposition (Mao and Wu 2007). In this paper, we apply the aperture correction in LAD to imaging in areas with irregular topography. We filled with near surface velocity in the area between the highest surface datum and the irregular surface. Based on the LCB beamlet propagator (Wu et al., 2000; Wang and Wu, 2002; Luo and Wu, 2003; Luo and Wu, 2005; Wu et al., 2008), continuation of the wavefield begins from the highest surface datum and seismic data are added where the level intersect receivers. At each depth, LEF decomposition was used to obtain the LWD image and aperture correction factors. And then transform them into LAD where amplitude correction is performed. In order to test the validity of our method, examples of amplitude correction for imaging using the typical irregular topography model Model94 (Gray and Marfurt, 1995) are shown. The image after amplitude correction has shown clearly improvement in deep area compared with the one with the image after AGC. Eliminating the influence of irregular topography during the wavfield downward continuation Based on the LCB beamlet propagator, wavefield continuation starts from the highest irregular surface horizontal datum. At each depth, the corresponding seismic data was added if there exist located receivers. For the source wavefield continuation, the source data will be added if source exist there. By this way, the influence of irregular surface can be eliminated during the process of continuation. Aperture correction in local dip-angle domain Local image matrix (LIM) calculated during the migration is distorted from local scattering matrix (LSM) due to the acquisition aperture limitation and propagation paths effects. The amplitude correction factors can be obtained in LAD (Wu et al., 2004) or LWD (Cao and Wu et al., 2008) to restore the LSM by the correction. Since it is more efficient to obtain the wavefield in the LWD than in the 1 Visiting from college of Geo-resources and Information, China University of Petroleum, Dongying, Shandong, , China 2 College of Geo-resources and Information, China University of Petroleum, Dongying, Shandong, , China 2758

2 LAD, we calculate the Green s function in the irregular topography acquisition system and obtain the amplitude factor in LWD. It can be written as equation (2), * Fw ξm, ) = 2 GI ξ m;,) GF ξ m; ) (2) 2 (, ; ) 1 dx A( x x ) g GF x ξ n xg { } 2 g, S Where stands for complex conjugate; x stand for z) ; ξ m and ξ n are the source and receiving wavenumber respectively; G I is the Green s function used in the imaging process; GF is the Green s function used in forward modeling; A ( x g, ) is the spatial receiver aperture for a given source. Then transform the amplitude factor matrix Fw z,ξ m, ) and image matrix Lw z,ξ m, ) into local dip-angle domain expressed as F a z,θ ) and L a z,θ ). The image matrix after amplitude correction can be expressed as follows, L z, θ ) = La z, θ )/( Fa + ε ) (3) where θ is the local dip-angle and ε is the damping factor for regularization. Aperture correction on irregular topography model We exemplify the method using the 2D Canadian overthrust synthetic dataset. This model consists of a number of faulted and folded layers. It is a typical mountainous region. Figure 1a and figure 1b are the velocity model and its elevation. The model is meters long and the highest elevation is nearly 1800m. The top of the model is in 2000m above the sea level and the bottom of the model is 8000m below sea level. So the total depth of the model is 10000m. The velocity in the model ranges from 3600 m/s to 6000m/s. There are 278 shots and the shot interval is 90 m; recorded time is 5 seconds; Trace spacing is 15 m and offset from m to 3600 m for all shots except roll-in and roll-out; maximum number of trace is 480. Shots and receivers all located at the irregular surface as blue line shown in Figure 1b which is the receiver distribution of the 141st shot. Figure 1c shows the original shot records, from which we can see the obvious distortion of the event caused by the irregular topography. We extrapolate downward the wavefield from the top of the model with LCB propagator. The images and factors are obtained in LWD (Cao and Wu, 2008) with LEF decomposition (Mao and Wu, 2007) and then transform them into local dip-angle domain where the aperture correction is performed. Figure 1: Irregular topography model. (a) is elevation of irregular surface; (b) is the velocity model; (c) is single shot records. As examples, figure 2,figure 3 and figure 4 show the -30, 0 and 30 degree dip-angle domain amplitude correction factor, image and image after For the reason of limited acquisition aperture, the deep layers don t have enough illumination resulting in weak image energy for deep targets (Figure 2b, figure 3b and figure 4b). After the aperture correction with the factor (figure 2a, figure 3a and figure 4a), the deep structure image has significant improvement (figure 2c, figure 3c and figure 4c). Even some of small faults have clearer images. We compare the image obtained from conventional oneway migration (Figure 6a), the image get from LCB migration (Figure 6b) has some improvement at the irregular surface area for the reason of windowed background reference velocity. Both of them have weak illumination in deep area. For comparison we compensate the image with vertical gain control AGC factor. Figure 5 is the AG factor distribution. We plot the image after AGC compensation (Figure 6c). After stack all the images with amplitude correction in local dip-angle domain, we obtain the final image as figure 6d shows. It is obvious that the amplitude balance and image quality is better than the 2759

3 Beamlet migration on irregular surface with acquisition-aperture correction single compensation with AGC and the deep structure image has significant improvement. Figure 3: The amplitude correction factor and image for 0 Figure 2: The amplitude correction factor and image for -30 Figure 4: The amplitude correction factor and image for 30 Figure 5: Amplitude compensation factor of vertical AGC 2760

4 Figure 7: comparison of the image amplitudes for a deep layer before and after amplitude correction: (a) layer location in model; (b) image amplitudes along a target surface before amplitude compensation; (c) image amplitudes after AGC; (d) image amplitudes after aperture correction. Conclusion Figure 6: The comparison of final image with different method: (a)the image using conventional one way migration; (b) the image using LCB beamlet migration; (c) the LCB migration image with vertical gain control AGC correction; (d)total strength of the image after acquisition aperture correction in the local dip-angle domain. We picked out the image amplitudes from the figure 6(b), 6(c) and 6(d) along a deep curved layer as showed in Figure 7(a) (arrow pointed layer). We see the strong variation of amplitude along the curved layer in figure 7(b) and 7(c) due to the difference in acquisition aperture response to different dips. After the correction in dip-angle domain figure 7(d), the image amplitudes are well balanced. We proposed a method to perform acquisition aperture correction in the local dip-angle domain for area with irregular topography. The irregular surface influence has been eliminated during the process of continuation. Because of the local reference velocity used in beamlet propagation, the image near the irregular surface has some improvement. After the aperture correction, the image quality in deep weak illumination area has been improved significantly. The test of Canadian overthrust irregular surface model illustrated the validity of our method. Acknowledgements: This research is sponsored by the WTOPI (Wavelet Transform On Propagation and Imaging for seismic exploration) Research Consortium at University of California, Santa Cruz. We thank Jian Mao, Bangyu Wu, Jun Cao, Haoran Ren for helpful discussions. We also thank Amoco and BP for the irregular topography model. 2761

5 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2009 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES 2762